Particle model of matter

What you'll learn

This topic covers how the particle model explains the properties and behaviour of solids, liquids and gases. You'll learn to calculate density, understand how heating substances changes their internal energy, and explain state changes using particle theory. This is a fundamental topic that links to many other areas of physics including energy stores and transfers.

Key terms and definitions

Density — the mass per unit volume of a substance, measured in kg/m³ or g/cm³

Internal energy — the total kinetic energy and potential energy of all the particles in a system

Specific heat capacity — the energy required to raise the temperature of 1 kg of a substance by 1°C, measured in J/kg°C

Specific latent heat — the energy required to change the state of 1 kg of a substance without changing its temperature, measured in J/kg

Specific latent heat of fusion — the energy required to change 1 kg of a substance from solid to liquid (or released when changing from liquid to solid) at constant temperature

Specific latent heat of vaporisation — the energy required to change 1 kg of a substance from liquid to gas (or released when changing from gas to liquid) at constant temperature

Brownian motion — the random movement of particles suspended in a fluid, caused by collisions with fast-moving particles in the fluid

Absolute zero — the theoretical temperature at which particles have minimum kinetic energy, equal to -273°C or 0 K

Core concepts

The particle model and states of matter

The particle model states that all matter is made up of tiny particles (atoms, molecules or ions). The arrangement, movement and energy of these particles determine whether a substance is solid, liquid or gas.

Solids:

• Particles arranged in a regular pattern
• Particles vibrate about fixed positions
• Strong forces of attraction between particles
• Cannot be compressed (particles already close together)
• Fixed shape and volume

Liquids:

• Particles close together but can move past each other
• Particles move randomly
• Moderate forces of attraction between particles
• Cannot be compressed significantly
• Fixed volume but take the shape of their container

Gases:

• Particles far apart and move randomly at high speeds
• Particles collide with each other and container walls
• Very weak forces of attraction between particles
• Can be compressed (large spaces between particles)
• No fixed shape or volume

The particle model is a simplification. It treats particles as solid spheres with no forces between them, which doesn't fully explain some real-world observations. However, it successfully explains many properties of matter at GCSE level.

Density calculations

Density relates the mass and volume of a substance using the equation:

ρ = m/V

Where:

• ρ (rho) = density in kg/m³ or g/cm³
• m = mass in kg or g
• V = volume in m³ or cm³

Converting units:

• 1 g/cm³ = 1000 kg/m³
• To convert cm³ to m³: divide by 1,000,000
• To convert g to kg: divide by 1000

Measuring density:

For regular solids:

1. Measure mass using a balance
2. Calculate volume using length measurements (e.g. V = l × w × h for a cuboid)
3. Use ρ = m/V

For irregular solids:

1. Measure mass using a balance
2. Measure volume using a displacement can (eureka can) — the volume of water displaced equals the volume of the object
3. Use ρ = m/V

For liquids:

1. Measure mass of empty measuring cylinder
2. Pour liquid into cylinder and record volume
3. Measure total mass
4. Subtract to find mass of liquid
5. Use ρ = m/V

Typical density values:

• Solids: 1000-20,000 kg/m³ (metals are dense, wood is less dense)
• Liquids: 800-1300 kg/m³ (water is 1000 kg/m³)
• Gases: 0.1-2 kg/m³ (much less dense than solids and liquids)

These values reflect particle arrangement. Gases have much lower density because particles are far apart.

Internal energy and temperature

Internal energy is the sum of:

• Kinetic energy of particles (due to their movement)
• Potential energy of particles (due to their positions and bonds)

Heating a substance increases its internal energy by:

• Increasing the kinetic energy of particles (temperature rises)
• Increasing the potential energy of particles (during state changes)

Temperature is a measure of the average kinetic energy of particles in a substance. When temperature increases, particles move faster on average.

Important distinction: Temperature measures the average kinetic energy per particle, while internal energy is the total energy of all particles in the system.

Specific heat capacity

When a substance is heated and its temperature changes (without changing state), the energy transferred is calculated using:

ΔE = m × c × Δθ

Where:

• ΔE = change in thermal energy in joules (J)
• m = mass in kilograms (kg)
• c = specific heat capacity in J/kg°C
• Δθ = change in temperature in °C or K

Specific heat capacity tells you how much energy is needed to raise the temperature of 1 kg of a substance by 1°C. Different substances have different specific heat capacities because:

• Particles have different masses
• Forces between particles vary
• Energy is distributed differently in different structures

Common specific heat capacities:

• Water: 4200 J/kg°C (high value — water heats up and cools down slowly)
• Concrete: 850 J/kg°C
• Copper: 385 J/kg°C
• Lead: 130 J/kg°C

Water's high specific heat capacity makes it useful for cooling systems and explains why coastal areas have milder climates than inland areas.

Investigating specific heat capacity:

Required practical method:

1. Measure mass of solid block (e.g. aluminium or copper)
2. Insert immersion heater and thermometer into drilled holes
3. Insulate block to reduce energy loss
4. Record initial temperature
5. Connect heater to power supply and joulemeter
6. Heat for measured time
7. Record final temperature and energy supplied
8. Use c = ΔE/(m × Δθ) to calculate specific heat capacity

Sources of error:

• Energy lost to surroundings (minimise with insulation)
• Not all energy from heater transfers to block
• Uneven heating of block

Changes of state and latent heat

When substances change state:

• Energy is transferred but temperature stays constant
• Bonds between particles are broken or formed
• Internal energy changes due to potential energy change

The key principle: During a state change, energy supplied increases potential energy (not kinetic energy), so temperature remains constant while the state changes.

State changes:

• Melting: solid → liquid
• Freezing: liquid → solid
• Boiling/evaporating: liquid → gas
• Condensing: gas → liquid
• Sublimation: solid → gas (e.g. solid carbon dioxide/dry ice)

Energy transferred during state changes:

E = m × L

Where:

• E = energy transferred in joules (J)
• m = mass in kilograms (kg)
• L = specific latent heat in J/kg

Two types of specific latent heat:

Specific latent heat of fusion (melting/freezing):

• Energy needed to change 1 kg between solid and liquid
• For water: 334,000 J/kg

Specific latent heat of vaporisation (boiling/condensing):

• Energy needed to change 1 kg between liquid and gas
• For water: 2,260,000 J/kg

Vaporisation requires more energy than fusion because:

• Particles must completely overcome all forces between them
• Particles move much further apart
• Much more work done against forces of attraction

Particle motion and gas pressure

Gas pressure is caused by particles colliding with container walls. Each collision exerts a tiny force. With billions of collisions per second, the total creates measurable pressure.

Increasing gas pressure:

• Increase temperature at constant volume — particles move faster, collide more frequently and with greater force
• Decrease volume at constant temperature — particles collide with walls more frequently
• Add more gas at constant volume and temperature — more particles mean more collisions

Brownian motion provides evidence for the particle model. When smoke particles are viewed in air using a microscope and bright light:

• Smoke particles move randomly in different directions
• Movement is caused by invisible air particles colliding with smoke particles
• Air particles move randomly and constantly
• Demonstrates that gases consist of particles in random motion

This observation supports the kinetic theory of matter and provides indirect evidence for the existence of atoms and molecules.

Temperature and absolute zero

The Kelvin scale is an absolute temperature scale where 0 K is the lowest possible temperature.

Absolute zero (0 K = -273°C) is the temperature at which particles have minimum kinetic energy. They cannot get any colder because you cannot have less than minimum kinetic energy. Particles still vibrate at absolute zero but with the minimum possible energy.

Converting between Celsius and Kelvin:

• Temperature in K = Temperature in °C + 273
• Temperature in °C = Temperature in K - 273

The Kelvin scale is used in gas law calculations because it's proportional to the average kinetic energy of particles. If you double the Kelvin temperature, you double the average kinetic energy.

Worked examples

Example 1: Density calculation

Question: A metal cube has sides of length 2.0 cm and a mass of 48 g. Calculate the density of the metal in g/cm³ and identify whether it could be aluminium (density 2.7 g/cm³) or iron (density 7.9 g/cm³). [4 marks]

Solution:

Step 1: Calculate volume V = l × w × h = 2.0 × 2.0 × 2.0 = 8.0 cm³ [1 mark]

Step 2: Use density equation ρ = m/V = 48/8.0 [1 mark]

Step 3: Calculate ρ = 6.0 g/cm³ [1 mark]

Step 4: Compare with given values The density is closer to aluminium than iron, but doesn't match either exactly. It could be an alloy or a different metal. [1 mark]

Example 2: Specific heat capacity

Question: A kettle heats 1.5 kg of water from 20°C to 100°C. Calculate the energy transferred to the water. The specific heat capacity of water is 4200 J/kg°C. [3 marks]

Solution:

Step 1: Identify values m = 1.5 kg, c = 4200 J/kg°C, Δθ = 100 - 20 = 80°C [1 mark]

Step 2: Write equation and substitute ΔE = m × c × Δθ = 1.5 × 4200 × 80 [1 mark]

Step 3: Calculate ΔE = 504,000 J = 504 kJ [1 mark]

Example 3: Latent heat

Question: Calculate the energy required to completely melt 0.5 kg of ice at 0°C. The specific latent heat of fusion for ice is 334,000 J/kg. Explain why the temperature does not change during melting. [4 marks]

Solution:

Step 1: Use equation E = m × L [1 mark]

Step 2: Substitute values E = 0.5 × 334,000 = 167,000 J [1 mark]

Step 3: Explain constant temperature During melting, energy supplied increases the potential energy of water particles [1 mark] as bonds between particles are broken, not the kinetic energy, so temperature (which depends on average kinetic energy) stays constant. [1 mark]

Common mistakes and how to avoid them

• Confusing mass and volume in density calculations — Always identify which quantity you have and which you need to find. Rearrange ρ = m/V correctly: m = ρV or V = m/ρ

• Using the wrong specific latent heat — Use latent heat of fusion for melting/freezing and latent heat of vaporisation for boiling/condensing. Check which state change is occurring

• Forgetting unit conversions — Always check if units match the equation requirements. Convert g to kg, cm³ to m³, or vice versa. Show conversion working in your answer

• Thinking temperature increases during state changes — Temperature stays constant during melting, boiling, freezing or condensing because energy changes potential energy (bonds) not kinetic energy (movement)

• Confusing temperature and internal energy — Temperature measures average kinetic energy per particle. Internal energy is the total kinetic and potential energy of all particles

• Stating particles stop moving at absolute zero — Particles have minimum kinetic energy at absolute zero but still vibrate. They cannot have zero energy

Exam technique for "Particle model of matter"

• Command words matter: "Calculate" requires a numerical answer with working. "Explain" requires reasons linking cause and effect. "Describe" requires stating what happens without detailed explanation

• Show all working in calculations — Write the equation, substitute values with units, then calculate. This allows for error-carried-forward marks even if you make an early mistake

• Link answers to the particle model — When explaining properties or changes, refer explicitly to particle arrangement, movement and forces. Use correct terminology: "particles" not "molecules" unless specified

• Check equation rearrangements — Common errors include incorrect rearrangement of ρ = m/V or ΔE = mcΔθ. Use triangle methods if helpful or write steps clearly

Quick revision summary

The particle model explains matter as particles in different arrangements and motion. Density (ρ = m/V) depends on particle packing. Heating increases internal energy — either raising temperature (ΔE = mcΔθ) or changing state (E = mL) at constant temperature. Specific heat capacity varies between substances. Latent heat changes potential energy during state changes. Gas pressure results from particle collisions. Absolute zero (-273°C) is the minimum possible temperature where particles have minimum kinetic energy.